The second pattern of the C Major scale uses the A shape open chord. When looking at the open A chord the root notes are on the open 5th string and at the 2nd fret of the 3rd string.
A
Reminder: The notes used in the C Major scale are C D E F G A B, there are no sharps or flats in the C Major scale.
So if we take a look at the scale on the fretboard, you will see something like the following pattern… the root notes are marked with the “X“…
| | $3.2.$4.2.$5.2 | $1.3.$2.3.$4.3.$5.X.$6.3 | $3.4 | $1.5.$2.5.$3.X.$4.5.$5.5.$6.5 | $2.6 |
Note: In the diagram above it’s the fret numbers that are indicated not the scale degrees, and it isn’t the way you would normally write out a scale using TAB, it’s just to illustrate the fingering pattern of the scale. 
When playing the scale on the guitar I normally start on the lowest pitch root note, 5th string 3rd fret, and play up to the highest pitch note of the scale, 1st string 5th fret, which is an A note.
| $5.3 5 $4.2 3 5 $3.2 4 5 $2.3 5 6 $1.3 5 |
Before descending back to the lowest pitch note of the scale, the G on the 3rd fret 6th string, then back up in pitch to the C root note on the 3rd fret 5th string.
| $1.5 3 $2.6 5 3 $3.5 4 2 $4.5 3 2 $5.5 3 2 $6.5 3 | $6.3 5 $5.2 3 |